CN108351432B - Data-driven focus inversion - Google Patents

Data-driven focus inversion Download PDF

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CN108351432B
CN108351432B CN201580084177.7A CN201580084177A CN108351432B CN 108351432 B CN108351432 B CN 108351432B CN 201580084177 A CN201580084177 A CN 201580084177A CN 108351432 B CN108351432 B CN 108351432B
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CN108351432A (en
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A·K·阮
F·A·马奥
T·维克
J·I·诺德斯卡格
E·考塞
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Equinor Energy AS
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Abstract

Data-driven focused inversion discloses a method of processing geophysical data acquired from a subsurface region. The method includes receiving geophysical data acquired from a subsurface region, determining data points that are highly sensitive to anomalies, performing an inversion based on the data points, wherein during the inversion, focusing on the anomalies is achieved by increasing weights of the data points, and determining at least one model of a distribution of physical properties in the subsurface region.

Description

Data-driven focus inversion
Technical Field
The present invention relates to geophysical exploration and data processing, and more particularly to a method for optimizing a physical property distribution model based on data acquired according to a geophysical exploration method (e.g., a controlled source electromagnetic or seismic survey).
Background
Geophysical data acquired from a subsurface region via conventional acquisition methods (e.g., seismic or CSEM or like surveys) may be used to obtain information about the distribution of physical properties in the subsurface region, so long as there is a mathematical relationship between the acquired data and the physical properties that are desired to be studied. Using the acquired data and a priori knowledge about the subsurface region, a model characterizing the distribution of the physical property may be generated. In this term, "model" refers to an estimated quantity. Inversion involves optimization of the generated model to determine the distribution of properties that explain the observed data.
The Inverse Problem (i.e. inverting Model parameters from the measured data set) is almost always an undetermined, non-unique and non-linear Problem (Tarantola, A. Inverse protocol Theory, Elsevier, New York 1987; Tarantola, A. Inverse protocol Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics 2005, and Zhdantv, M.S. geographic analysis Theory and Regulation schemes, Elsevier 2002). The measurement data does not provide enough information to ensure a unique solution at the desired resolution. Furthermore, the measurement data is also always affected by noise, inaccuracies and errors. Finally, the implementations of forward modeling operators required by inversion engines often have limited accuracy because they are based on assumptions for practical and computational reasons. To obtain a solution, artificial constraints and regularization on the model parameters are usually introduced to stabilize the inverse problem (Tarantola, 2005 and Zhdanov 2002). The assumptions behind these constraints and regularization are often inaccurate.
The resulting final inversion model is therefore a compromise between all these constraints, inaccuracies and errors. In practice, the inversion process always ends in an attraction domain with corresponding local minima, which favors certain parts and aspects of the inverse model while sacrificing other parts and aspects of the model. Which attraction domain and corresponding local minimum the inversion run actually ends with depends on the initial model, the regularization parameters, the included data points, the weights of the individual data points, and the optimization algorithm used. Without adding very strong assumptions/constraints, the results of this struggle between different inversion driving forces are difficult to control, potentially leading to severe artifacts in the inversion results if the assumptions are not accurate.
It is often desirable to reconstruct certain portions and aspects of the model as accurately as possible. The cost of a less accurate reconstruction of other less important parts/aspects of the model may then be accepted. Typically, the size of the survey object is very small compared to the entire model to be inverted. Correspondingly, the number of data points that are mainly sensitive to the large model background is completely dominant compared to several data points that are actually sensitive to the target. Thus, the target response tends to be too weak to compete with the other much stronger inversion driving forces, which results in poor target imaging and reasonably good background imaging.
As mentioned above, constraints and regularization are conventionally used to focus the inversion search space and results (Tarantola and ZHdanov 2002), for example, to encourage the inversion engine to promote certain aspects of the inversion model, such as smoothness, density anomalies, low/high values for certain portions of the model (Tarantola and ZHdanov 2002). Hereafter, we use the term regularization to denote both constraint and regularization. This conventional approach is model-driven focused inversion (MDFI): which applies directly to the attributes of the model. The problem with this model-driven regularization is that the inverse model is forced to contain the properties required for regularization, whether or not those properties are present in the real model.
The model-driven focus inversion (MDFI) method can be shown as follows. Let the inversion/optimization problem find the M-dimensional model vector that minimizes the following mismatch function
Figure BDF0000011679660000021
Figure BDF0000011679660000022
Here, the data residual
Figure BDF0000011679660000023
Wherein the content of the first and second substances,
Figure BDF0000011679660000024
is a real or complex N-dimensional vector representing the measured data, and
Figure BDF0000011679660000025
is used for model
Figure BDF0000011679660000026
Forward modeling data. Sign of reverse vector
Figure BDF0000011679660000027
Representing a conjugate transpose. Data covariance matrix
Figure BDF0000011679660000028
Data errors and their dependencies are described. Conventionally, the pairs are formed by diagonal matrices containing data variances
Figure BDF0000011679660000029
An approximation is made. Diagonal line
Figure BDF00000116796600000210
Indicating that all data points are irrelevant. Conventional used in geophysical inversion
Figure BDF00000116796600000211
Examples of (ii) can be found in (Morten, j.p.,
Figure BDF00000116796600000212
A.K.,
Figure BDF00000116796600000213
t. (2009) CSEM data undirected analysis for 3D inversion, SEG Expanded isolates 28,724).
Regularizing mismatch functions
Figure BDF00000116796600000214
Only depending on the model parameters. λ is a real scalar used to control the strength of the model regularization term. Typically, the technician uses
Figure BDF0000011679660000031
To stabilize the inverse problem and control the inversion flow, i.e. to force/encourage the inverse model to have certain properties, such as smoothness, sharpness, parameters that remain within boundaries, proximity to a certain priority model, etc. (Tarantola, 2005 and Zhdanov, 2002).
Disclosure of Invention
A data-driven focus inversion (DDFI) method is proposed that encourages the inversion optimizer to focus more on certain specific attributes, parameters, regions of the inversion model while sacrificing other attributes, parameters, and regions. Unlike MDFI, DDFI does not force the inversion model to contain the focused attributes if they are not present in the data.
According to a first aspect of the present invention there is provided a method of processing geophysical data acquired from a subsurface region, the method comprising: receiving geophysical data acquired from a subsurface region; determining data points of the geophysical data that are highly sensitive to anomalies; performing an inversion based on the geophysical data, wherein during the inversion, focusing on the anomaly is achieved by increasing a weight of the data points, wherein increasing the weight of the data points is achieved by: defining a covariance matrix
Figure BDF0000011679660000032
Which is prepared from
Figure BDF0000011679660000033
The function of (a), wherein,
Figure BDF0000011679660000034
is a focus matrix and alpha is a constant for controlling the focus intensity, and adding for the data points
Figure BDF0000011679660000035
Wherein simulated geophysical data generated by forward modeling from two models of a subsurface region are compared, the data points are determined, and a focus matrix is constructed
Figure BDF0000011679660000036
Wherein the two models are the same except for the anomaly; and determining at least one model of the distribution of physical properties in the subsurface region from the inversion.
According to a second aspect of the present invention there is provided a method of processing geophysical data acquired from a subsurface region, the method comprising: receiving geophysical data acquired from the subsurface region; determining data points of the geophysical data that have low sensitivity to anomalies; based on said geophysical numberPerforming an inversion, wherein during the inversion, focusing on the anomaly is achieved by reducing a weight of the data points, wherein reducing the weight of the data points is achieved by: defining a covariance matrix
Figure BDF0000011679660000037
Which is prepared from
Figure BDF0000011679660000038
The function of (a), wherein,
Figure BDF0000011679660000039
is a focus matrix and alpha is a constant for controlling the focus intensity, and adding for the data points
Figure BDF00000116796600000310
Wherein simulated geophysical data generated by forward modeling from two models of a subsurface region are compared, the data points are determined, and a focus matrix is constructed
Figure BDF00000116796600000311
Wherein the two models are the same except for the anomaly; and determining at least one model of the distribution of physical properties in the subsurface region from the inversion.
According to a third aspect of the present invention, there is provided an apparatus for processing data, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method as described above when executing the computer program.
According to a fourth aspect of the present invention there is provided an apparatus for processing data, comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized in that said apparatus for processing data comprises or is programmed by a computer program as described above.
According to a fifth aspect of the present invention, there is provided a computer-readable storage medium characterized in that the computer-readable storage medium stores the computer program as described above.
According to a sixth aspect of the present invention, there is provided a method of transmitting a program over a network, characterized in that propagated over the network is a computer program as described above.
Drawings
FIG. 1 shows the verticality (R) of the first and second forward modelsV) And level (R)H) The resistivity is abnormal.
FIG. 2 shows the electric field amplitude (E) of an azimuth receiverxSolid line), phase (point), and noise estimate.
FIG. 3 shows the axial component E of a drag chainxFocus matrix with index n of 1/2 and f of 1Hz
Figure BDF0000011679660000041
Is provided.
Fig. 4 shows a real model T, an initial model C, an α -0 inverted vertical resistivity model, and an α -20 inverted vertical resistivity model.
Fig. 5 shows a real model T, an initial model C, an α -0 inverted horizontal resistivity model, and an α -20 inverted horizontal resistivity model.
Fig. 6 shows an inverted vertical resistivity model inverted with α -0 and α -20 for the real model B, the initial model C.
Fig. 7 shows an inverted vertical resistivity model inverted with α -0, α -5, and α -20 for the initial model C.
Fig. 8 shows the vertical resistivity model inverted with α -0 and α -5 for the real model T, the initial model D.
Fig. 9 shows the vertical resistivity model inverted with α -0 and α -20 for the real model T, the initial model E.
FIG. 10 shows a flow chart of an exemplary method.
FIG. 11 schematically illustrates, in block diagram form, an exemplary computer device.
FIG. 12 is a schematic diagram of a computer system for implementing one or more embodiments of the invention.
Detailed Description
The method according to the invention implements a geophysical data processing technique to generate a physical property distribution model of the subsurface region. Geophysical data acquired from a geophysical survey and a priori knowledge about the subsurface region are used to generate a model that characterizes the distribution of physical properties that produced the acquired data.
Some data points are highly sensitive to certain parameters, property regions/parts of the model. By increasing the weight of these data points during the inversion process, a more accurate physical property distribution model can be achieved, e.g., properties not present in the data do not become part of the inversion model.
Inversion involves adding new terms to the covariance matrix to encourage the inversion engine to focus its efforts on minimizing mismatch of selected data residuals that are highly sensitive to certain parameters, properties, regions/portions of the model. Hereafter, we will use the term object to denote a parameter, property or region/portion of the desired model we wish to study. We introduce a modified covariance matrix, which is defined as:
Figure BDF0000011679660000051
here, the first and second liquid crystal display panels are,
Figure BDF0000011679660000052
is a modified covariance matrix that is,
Figure BDF0000011679660000053
is a matrix of units, and is,
Figure BDF0000011679660000054
is the focus matrix and alpha is a constant used to control the focus intensity. In order to achieve focusing on the target,
Figure BDF0000011679660000055
should be defined as small/zero for data points that are not sensitive to the target and large for data points that are sensitive to the target. To achieve focus on the target, assume (given) is in the matrix
Figure BDF0000011679660000056
The most sensitive data points should have a higher weight (higher focus) than the data points that are not sensitive to the target.
In another embodiment of the invention, the focusing matrix may also be used in the reverse sense, i.e. will
Figure BDF0000011679660000057
Defined as small for data points that are sensitive to certain parameters, attributes, regions of the inverse model and large at the remaining data points. This encourages the inversion engine to focus on non-target portions with minimal effort. This inverse approach can be used to reduce the influence of extraneous parts of the model in the inversion. Depending on the purpose of the inversion study, the "extraneous" part of the model may be, for example, salt, basalt, pipeline, etc.
For constructing
Figure BDF0000011679660000061
By means of a scattered field. Here two forward simulations are performed: once for background model
Figure BDF0000011679660000062
With analog data
Figure BDF0000011679660000063
Is used for model at a time
Figure BDF0000011679660000064
Which contains the same background model with the added target. The scattered field is then defined as:
Figure BDF0000011679660000065
therefore, the temperature of the molten metal is controlled,
Figure BDF0000011679660000066
is a data response from the target only. Then, the user can use the device to perform the operation,
Figure BDF0000011679660000067
can be defined, for example, as:
Figure BDF0000011679660000068
Figure BDF0000011679660000069
is a user-supplied matrix function that may be, for example,
Figure BDF00000116796600000610
where n is an index provided by the user.
Figure BDF00000116796600000611
A matrix function of the scattered field provided to the user, for example:
Figure BDF00000116796600000612
wherein the content of the first and second substances,
Figure BDF00000116796600000613
to represent
Figure BDF00000116796600000614
And the matrix function diag () extracts the diagonal matrix.
It is to be noted that it is preferable that,
Figure BDF00000116796600000615
the form ensures defocusing of the noise data points.
For diagonal line
Figure BDF00000116796600000616
And
Figure BDF00000116796600000617
the effect of equation 7 is very similar to increasing the weight of the data points where the scattered field is strongest.
By way of example, a synthetic dataset may be used to show the effectiveness of the invention, and showing that data-driven focused inversion methods improve the inversion results around the target; the method is applicable to inversion of synthetic seafloor logging Controlled Source Electromagnetic (CSEM) datasets.
Electromagnetic data consists of electric and magnetic fields: are each [ Ex,Ey,Ez]And [ Hx,Hy,Hz]. The components of the electromagnetic field vector are complex in the frequency domain and depend on the source(s), receiver (r) and frequency (f), e.g. Ex→Ex(s,r,f)。
Conventionally, the data covariance matrix used in CSEM inversion is assumed to be diagonal with the elements given by the data uncertainty factor, an example may be found in (Morten, 2009;
Figure BDF0000011679660000071
f.a. and Nguyen, a.k.enhanced surface response for marine CSEM rendering, Geophysics, No. 75, pages 7-10, 2010). Here we define the variance for different electromagnetic fields as:
|ΔEx|2＝|β1Ex|2+|β2Ey|2+|β3Ez|2+|ηEx|2
|ΔEy|2＝|β2Ex|2+|β1Ey|2+|β3Ez|2+|ηEy|2
|ΔEz|2＝|β3Ex|2+|β3Ey|2+|β1Ez|2+|ηEz|2
|ΔHx|2＝|β1Hx|2+|β2Hy|2+|β3Hz|2+|ηHx|2
|ΔHy|2＝|β2Hx|2+|β1Hy|2+|β3Hz|2+|ηHy|2
|ΔHz|2＝|β3Hx|2+|β3Hy|2+|β1Hz|2+|ηHz|2
wherein, beta1Is the autocorrelation multiplication uncertainty between the field components, and beta2And beta3Is the cross-correlation multiplication uncertainty between the field components. In addition, η is the field additive noise alone. Maao and Nguyen (2010) provide the reasons and explanations behind multiplicative uncertainty and additive noise. Thus, a single i- (source, receiver, frequency) measurement is a data vector
Figure BDF0000011679660000072
Up to 6 additional components are provided, and then the corresponding diagonal covariance matrix for the electric field portion is:
Figure BDF0000011679660000073
similarly, for the magnetic field:
Figure BDF0000011679660000074
synthetic data examples
In this section we will show that the data-driven focus inversion method is well suited for 3D anisotropic inversion on synthetic seafloor logging controlled source electromagnetic data sets.
The synthetic model and synthetic dataset are largely generated from measured data from a real survey. The synthetic model is created using the true seismic horizons at the survey location. Seismic-driven CSEM inversion from real datasets (Nguyen, a.k.,
Figure BDF0000011679660000081
hansen J.O (2013) CSEM expansion in the Barents Sea, Part II-High resolution CSEM inversion,75th annular Conference and expansion, EAGE, Extended extracts, We 0403). Fig. 1 shows slices of a real model (T) and a background model (B). The model T has a vertical resistivity R thereinVAn anomaly; while no anomalies exist in model B. This R in the real modelVAnomalies are the target of inversion studies. Horizontal resistivity model RHThe same for both model T and model B. RHThe reason behind the lack of anomalies in (A) is due to the fact that thin horizontal resistive anomalies have virtually no effect on the CSEM data, so R is not constructed in the seismic-driven CSEM inversionHAnd (6) abnormal. We believe that it is not necessary to artificially associate R withHAnomalies are added to the real model. 3D forward modeling with grid dx-dy-100 m and dz-40 m is based on the finite difference time domain method (
Figure BDF0000011679660000082
F.A (2007) Fast fine-difference time-domain modifying for marine-surface electronic schemes, geophisics, 72, A19-23). Data were collected for frequencies f of 0.25Hz, 0.5Hz, 1 Hz. The water depth measurements are taken into account in the modelling.
The navigation and orientation of the transmitter and receiver is taken from the survey data. For each synthetic data point, we add to it a complex number with a random phase and an amplitude given by the noise estimate for the corresponding real data point. Furthermore, we distort the receiver orientation values by uniformly distributing random numbers between-3 and 3 degrees. Thus, noise levels, receiver rotation errors, navigation defects are all close to the uncertainty and condition of the true acquisition. The electric field of the azimuth line affected by noise is shown in fig. 2. We see that additive noise can significantly affect the data in both amplitude and phase, particularly where offsets of the magnetotelluric pulse train occur.
In order to construct a covariance matrix of the focus of the object, the sensitivity of each data point to the object needs to be estimated. This can be achieved by comparing clean synthetic data from model T and model B.
Figure BDF0000011679660000083
The axial component E of a drag chain is shown in FIG. 3xFocus matrix with index n of 1/2 and f of 1Hz
Figure BDF0000011679660000084
Is provided. We see that the target clearly projects its presence and information into a limited set of data points.
Inversion
The L-BFGS-B regimen (Zach, J.J.,
Figure BDF0000011679660000091
A.K.,
Figure BDF0000011679660000092
t, and
Figure BDF0000011679660000093
3D inversion of marine CSEM data using a fast fine-difference time-domain forward code and adaptive theory-based optimization SEG Expanded abstract 27,614,2008) was used to invert the synthetic datasets from model T and model B. No regularization is applied in this pixel-based focus inversion. The initial model C is a smooth and enlarged version of model B with dx-dy-150 m and dz-40 m. For inversion, we use field ExAnd EyAnd the frequency f is 0.25Hz, 0.5Hz, 1Hz, the corresponding maximum absolute deviation is 10000m, 900 Hz0m, 8000 m. The minimum offset is 1500m for all frequencies. The final inversion result is obtained from iteration 100, unless explicitly mentioned.
Fig. 4 shows a real, initial model C, an α -0 inverted vertical resistivity model, and an α -20 inverted vertical resistivity model. We see that the model of the α ═ 0 inversion contains anomalies at the correct locations. However, the reconstructed anomaly is rather weak if the resistivity is too low. Furthermore, we see that the model of the α ═ 20 inversion reconstructs the anomaly much better than the conventional inversion. The difference in resolution between the real model and the inverse model stems from the fact that: the true model is based on seismic guided inversion, where the inverted model is a pure CSEM data driven pixel-based inversion with much lower resolution than the seismic guided case.
Fig. 5 shows a true, initial model C, an α -0 inverted horizontal resistivity model, and an α -20 inverted horizontal resistivity model. We see that the inverse model is more or less identical and very similar to the initial model. Even the receiver footprint is more or less identical. Most likely, these receiver footprints are the footprints of the introduced errors in the receiver direction. Again, it is noted that the introduction of thin, high resistance anomalies in the true horizontal model does not affect the data and thus the inversion results.
The question naturally asked is whether the weight of the focus anomaly may introduce artificial anomalies in the inversion results, even when there are no such anomalies in the input data. Fig. 6 shows an inverse model for α -0 and α -20 from dataset B. Here, the real model has no resistivity anomaly. We see that all inversions correctly predict the absence of resistivity anomalies in the model. Thus, it can be concluded that: the weight of the focus anomalies does not artificially introduce resistivity anomalies that are not present in the input data.
Fig. 7 shows the inverted vertical resistivity model for α -0, α -5 and α -20. It can be seen that improving focus also improves the clarity of resistivity anomalies in the inverse model.
Another natural problem isHow can a significantly wrong initial model affect the inversion results when applying weights for focus anomalies? We investigated this problem by performing an inversion with initial models D and E, which are distorted versions of the "correct" initial model C. The initial model D is RV→RVX 0.8 and RH→RHModified version of model C by 0.8.
Fig. 8 shows the vertical resistivity model for the following cases: true, original model D, inverted with α ═ 0, and inverted with α ═ 5. We see that when focused weights are used in the inversion, the resistivity anomaly is again recovered much better than the conventional unfocused weights. The inverted horizontal resistivity models corresponding to the model shown in fig. 8 are more or less identical.
Fig. 9 shows the vertical resistivity model for the following cases: true, initial model E, inverted with α ═ 0, and inverted with α ═ 5. The initial model E is RV→RVX 1.2 and RH→RHModified version of model C by 1.2. We see that when focused weights are used in the inversion, the resistivity anomaly is again recovered much better than the conventional unfocused weights. The inverted horizontal resistivity models corresponding to the model shown in fig. 8 are more or less identical.
Thus, it can be concluded that: a significantly wrong initial model does not reduce the effect of the weighting of the focus anomalies.
Above we have shown that the data-driven focus inversion (DDFI) method is well suited for CSEM inversion.
Unlike conventional model-driven focus inversion (MDFI) methods, DDFI does not impose certain properties into the inverted model if the presence of these properties is not present in the data.
Inversion of the measurement data often provides results with a lower resolution than required for interpretation, or the estimated parameters have a higher uncertainty than required, especially for a small target area or a small set of important parameters. Data-driven focused inversion places more effort on reducing the data residuals of selected data points that are sensitive to user-defined targets. Recall that the term object herein refers to selected attributes, parameters and regions of the model. The inversion results will therefore provide better clarity of the target at the expense of a generally acceptably poor background from the user's perspective.
The inversion almost always ends with a local minimum. Which minimum it ends with depends on the initial model, regularization, optimizer algorithm. Model-driven focus inversion enforces the properties indicated by the regularization term into the inversion model, e.g., a smooth regularization term forces the inversion model to be smooth regardless of the measured data. In contrast, data-driven focus inversion only puts more effort on reducing the data residuals for selected data points. Thus, if no target response is found in the measurement data, the focus function for the target does not force the inverse model to contain the target. Conversely, DDFI will ensure that the inverse model does not contain targets in this case, since the weighted data mismatch will be too high. Therefore, DDFI increases the probability that the inversion ends with a local minimum, which ensures that the properties of the target are accurately described.
Data-driven focus inversion DDFI attempts to find a model that minimizes the data fit for selected data points that are sensitive to a target, at the expense of other data points that are only sensitive to background and not to the target. This enables a more accurate definition of the target.
Fig. 10 is a flowchart illustrating exemplary steps according to the first embodiment. The following numbering corresponds to that of fig. 10:
s1, receiving geophysical data collected from a subsurface region.
And S2, determining data points with high abnormal sensitivity.
S3, performing inversion based on the data points, wherein during the inversion, focusing on the anomaly is achieved by increasing the weight of the data points.
S4, determining at least one model of physical attribute distribution in the underground region.
FIG. 11 is a flowchart showing exemplary steps according to a second embodiment; the following numbering corresponds to that of fig. 11:
s5, receiving the geophysical data collected from the underground area.
And S6, determining data points with low abnormal sensitivity.
S7, performing inversion based on the data points, wherein during the inversion, focusing on the anomaly is achieved by reducing the weight of the data points.
S8, determining at least one model of physical attribute distribution in the underground region.
Referring to FIG. 12, an exemplary computer device 1 capable of performing a method of processing geophysical data acquired from a subsurface region is provided, as described in an embodiment of the present invention. The computer device may contain or be programmed by a computer program 2, the computer program 2 comprising computer readable instructions for processing geophysical data acquired from a subsurface region, as described in embodiments of the invention. The computer program 2 may be stored on a non-transitory computer readable medium in the form of a memory 3. The computer program 2 may be provided from an external source 4. The computer device 1 may comprise a display 5 allowing a user to visualize the model of the distribution of the physical property in the determined subsurface region.

Claims (14)

1. A method of processing geophysical data acquired from a subsurface region, the method comprising:
receiving geophysical data acquired from a subsurface region;
determining data points of the geophysical data that are highly sensitive to anomalies;
performing an inversion based on the data points, wherein during the inversion, focusing on the anomaly is achieved by increasing a weight of the data points, wherein increasing the weight of the data points is achieved by:
defining a covariance matrix
Figure FDA0003295094960000011
Which is prepared from
Figure FDA0003295094960000012
The function of (a), wherein,
Figure FDA0003295094960000013
is a focus matrix and alpha is a constant for controlling the focus intensity, an
Adding for said data point
Figure FDA0003295094960000014
Wherein simulated geophysical data generated by forward modeling from two models of a subsurface region are compared, the data points are determined, and a focus matrix is constructed
Figure FDA0003295094960000015
Wherein the two models are the same except for the anomaly; and
at least one model of a distribution of physical properties in the subsurface region is determined from the inversion.
2. The method of claim 1, wherein the geophysical data is any one of electromagnetic data, seismic data, gravity data, or resistivity data.
3. The method of claim 2, wherein the electromagnetic data is controlled-source electromagnetic data.
4. The method of claim 1 or 3, wherein the covariance matrix
Figure FDA0003295094960000016
The method is realized by the following forms:
Figure FDA0003295094960000017
wherein the content of the first and second substances,
Figure FDA0003295094960000018
is a matrix of the covariance of the data,
Figure FDA0003295094960000019
is an identity matrix.
5. The method of claim 1, wherein the anomaly is a parameter of the at least one model.
6. The method of claim 5, wherein the parameter of the at least one model is a property of the at least one model.
7. A method of processing geophysical data acquired from a subsurface region, the method comprising:
receiving geophysical data acquired from the subsurface region;
determining data points of the geophysical data that have low sensitivity to anomalies;
performing an inversion based on the data points, wherein during the inversion, focusing on the anomaly is achieved by reducing a weight of the data points, wherein reducing the weight of the data points is achieved by:
defining a covariance matrix
Figure FDA0003295094960000021
Which is prepared from
Figure FDA0003295094960000022
The function of (a), wherein,
Figure FDA0003295094960000023
is a focus matrix and alpha is a constant for controlling the focus intensity, an
Adding for said data point
Figure FDA0003295094960000024
Wherein simulated geophysical data generated by forward modeling from two models of a subsurface region are compared, the data points are determined, and a focus matrix is constructed
Figure FDA0003295094960000025
Wherein the two models are the same except for the anomaly; and
at least one model of a distribution of physical properties in the subsurface region is determined from the inversion.
8. The method of claim 7, wherein the geophysical data is any one of electromagnetic data, seismic data, gravity data, or resistivity data.
9. The method of claim 8, wherein the electromagnetic data is controlled-source electromagnetic data.
10. The method of claim 7 or 8, wherein the covariance matrix
Figure FDA0003295094960000029
The method is realized by the following forms:
Figure FDA0003295094960000026
wherein the content of the first and second substances,
Figure FDA0003295094960000027
is a matrix of the covariance of the data,
Figure FDA0003295094960000028
is an identity matrix.
11. The method of claim 7, wherein the anomaly is a parameter of the at least one model.
12. The method of claim 11, wherein the parameter of the at least one model is a property of the at least one model.
13. An apparatus for processing data, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method as claimed in claim 1 when executing the computer program.
14. A computer-readable storage medium, characterized in that the computer-readable storage medium stores the computer program of claim 13.
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